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Blow-Up and Decay Estimate in a Logarithmic p-Laplace Parabolic Equation LI Ping, LI Feng-jie Chinese Quarterly Journal of Mathematics    2024, 39 (4): 331-354.   DOI: 10.13371/j.cnki.chin.q.j.m.2024.04.001 Abstract （187）      PDF（pc） （462KB）（96）       Knowledge map    Save This paper deals with an initial-boundary value problem of a fourth-order parabolic equation involving Logarithmic type p-Laplacian, which could be proposed as a model for the epitaxial growth of thin films. By using the variational method and the logarithmic type Sobolev inequality, we give some threshold results for blow-up solutions and global solutions, which could be classified by the initial energy. The asymptotic estimates about blow-up time and decay estimate of weak solutions are obtained. Related Articles | Metrics

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Local Existence and Blow-Up of Solutions for Pseudo-Parabolic Equation with Singular Potential and General Nonlinearity JIANG Dong-yue, TANG Zhong-hua, FANG Shao-mei Chinese Quarterly Journal of Mathematics    2024, 39 (2): 111-127.   DOI: 10.13371/j.cnki.chin.q.j.m.2024.02.001 Abstract （106）      PDF（pc） （465KB）（74）       Knowledge map    Save In this paper, a semilinear pseudo-parabolic equation with a general nonlinearity and singular potential is considered. We prove the local existence of solution by Galerkin method and contraction mapping theorem. Moreover, we prove the blow-up of solution and estimate the upper bound of the blow-up time for J(u0)≤0. Finally, we prove the finite time blow-up and estimate the upper bound of blow-up time for J(u0)>0. Related Articles | Metrics

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Complete Co-Homogeneity One K¨ahler Metrics on the Affine Quadric of Complex Dimension Two (Related to a Cohomogeneity One Point of View on a Yau Conjecture)#br# GUAN Daniel, LIANG Meng-xiang Chinese Quarterly Journal of Mathematics    2024, 39 (2): 200-220.   DOI: 10.13371/j.cnki.chin.q.j.m.2024.02.008 Abstract （95）      PDF（pc） （387KB）（49）       Knowledge map    Save  In this paper, we revisit the K¨ahler structures on the affine quadrics M1={z12 +z22 +z32 = 1} in the paper by Bo Yang and Fang-Yang Zheng. We found that theK¨ahler structures on the complex surface are more complicated than what they havethought. We shall also give some detail calculations and found that our results fit quitewell with earlier papers of the first author, one of them with X. X. Chen. Related Articles | Metrics

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Discontinuous Galerkin Method for Hydrodynamic and Sediment Transport Model ZHANG Ren-peng, WANG Bo, WANG Qiang, Chinese Quarterly Journal of Mathematics    2024, 39 (4): 355-365.   DOI: 10.13371/j.cnki.chin.q.j.m.2024.04.002 Abstract （85）      PDF（pc） （1085KB）（39）       Knowledge map    Save In this article, we propose and research a first-order, linearized discontinuous Galerkin method for the approximation of the hydrodynamic and sediment transport model. The method is decoupled and fully discrete, and is shown to be unconditionally stable. Furthermore, error estimates are proved. Finally, the theoretical analysis is confirmed by numerical examples. Related Articles | Metrics

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Sure Independence Screening via Semiparameteric Copula Learning XIN Xin, XIE Bo-yi, LIU Ke-ke Chinese Quarterly Journal of Mathematics    2024, 39 (2): 144-160.   DOI: 10.13371/j.cnki.chin.q.j.m.2024.02.003 Abstract （80）      PDF（pc） （393KB）（59）       Knowledge map    Save  This paper is concerned with ultrahigh dimensional data analysis, which has become increasingly important in diverse scientific fields. We develop a sure independence screening procedure via the measure of conditional mean dependence based on Copula (CC-SIS, for short). The CC-SIS can be implemented as easily as the sure independence screening procedures which respectively based on the Pearson correlation, conditional mean and distance correlation (SIS, SIRS and DC-SIS, for short) and can significantly improve the performance of feature screening. We establish the sure screening property for the CC-SIS, and conduct simulations to examine its finite sample performance. Numerical comparison indicates that the CC-SIS performs better than the other two methods in various models. At last, we also illustrate the CC-SIS through a real data example. Related Articles | Metrics

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On the Method of Solution for the Non-Homogeneous Generalized Riemann-Hilbert Boundary Value Problems ZHANG Wen-wen, LI Ping-run Chinese Quarterly Journal of Mathematics    2024, 39 (3): 262-269.   DOI: 10.13371/j.cnki.chin.q.j.m.2024.03.004 Abstract （76）      PDF（pc） （321KB）（38）       Knowledge map    Save This paper studies the non-homogeneous generalized Riemann-Hilbert (RH) problems involving two unknown functions. Using the uniformization theorem, such problems are transformed into the case of homogeneous type. By the theory of classical boundary value problems, we adopt a novel method to obtain the sectionally analytic solutions of problems in strip domains, and analyze the conditions of solvability and properties of solutions in various domains. Related Articles | Metrics

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Combinatorial Identities Concerning Harmonic Numbers CHEN Yu-lei, GUO Dong-wei Chinese Quarterly Journal of Mathematics    2024, 39 (3): 307-314.   DOI: 10.13371/j.cnki.chin.q.j.m.2024.03.008 Abstract （72）      PDF（pc） （295KB）（46）       Knowledge map    Save In this paper, we firstly establish a combinatorial identity with a free parameter x, and then by means of derivative operation, several summation formulae concerning classical and generalized harmonic numbers, as well as binomial coefficients are derived. Related Articles | Metrics

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Codimension-Two Bifurcations Analysis of a Discrete Predator-Prey Model Incorporating a Prey Refuge PANG Ru-yi, CHEN Qiao-ling Chinese Quarterly Journal of Mathematics    2024, 39 (2): 128-143.   DOI: 10.13371/j.cnki.chin.q.j.m.2024.02.002 Abstract （71）      PDF（pc） （842KB）（65）       Knowledge map    Save  In this paper, a discrete predator-prey model with prey refuge is investigated. It is proved that the model undergoes codimension-2 bifurcations associated with 1:2 and 1:3 resonances. The bifurcation diagrams and phase portraits show that the model has some interesting complex dynamical behaviors, such as limit cycle, periodic solutions, chaos and codimension-1 bifurcations. Related Articles | Metrics

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Pseudo S-Asymptotically (ω,c)-Periodic Solutions to Fractional Differential Equations of Sobolev Type MAO Hang-ning, CHANG Yong-kui Chinese Quarterly Journal of Mathematics    2024, 39 (3): 295-306.   DOI: 10.13371/j.cnki.chin.q.j.m.2024.03.007 Abstract （70）      PDF（pc） （402KB）（28）       Knowledge map    Save In this paper, we firstly recall some basic results on pseudo S-asymptotically (ω,c)-periodic functions and Sobolev type fractional differential equation. We secondly investigate some existence of pseudo S-asymptotically (ω,c)-periodic solutions for a semilinear fractional differential equations of Sobolev type. We finally present a simple example. Related Articles | Metrics

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Upper Bounds on the Aα Spectral Radius of Irregular Weighted Digraphs XI Wei-ge, XU Tao Chinese Quarterly Journal of Mathematics    2024, 39 (2): 161-170.   DOI: 10.13371/j.cnki.chin.q.j.m.2024.02.004 Abstract （67）      PDF（pc） （345KB）（34）       Knowledge map    Save  Let D be a weighted digraph with n vertices in which each arc has been assigned a positive number. Let A(D) be the adjacency matrix of D and W(D) = diag(w1+,w2+,...,wn+). In this paper, we study the matrix Aα(D), which is defined as Aα(D) =αW(D)+ (1−α)A(D), 0≤α≤1. The spectral radius of Aα(D) is called the Aα spectral radius of D, denoted by λα(D). We obtain some upper bounds on the Aα spectral radius of strongly connected irregular weighted digraphs. Related Articles | Metrics

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Italian Domination of Strong Product of Two Paths WEI Li-yang, LI Feng Chinese Quarterly Journal of Mathematics    2024, 39 (3): 221-234.   DOI: 10.13371/j.cnki.chin.q.j.m.2024.03.001 Abstract （65）      PDF（pc） （392KB）（50）       Knowledge map    Save The domination problem of graphs is an important issue in the field of graph theory. This paper mainly considers the Italian domination number of the strong product between two paths. By constructing recursive Italian dominating functions, the upper bound of its Italian domination number is obtained, and then a partition method is proposed to prove its lower bound. Finally, this paper yields a sharp bound for the Italian domination number of the strong product of paths. Related Articles | Metrics

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Fekete-Szegö Inequalities and the Symmetric Toeplitz Determinants for Certain Analytic Function Class Involving q-Differintegral Operator PEI Ke-ke, LONG Pin-hong, LIU Jin-lin, GANGADHARAN Murugusundaramoorthy Chinese Quarterly Journal of Mathematics    2024, 39 (4): 366-378.   DOI: 10.13371/j.cnki.chin.q.j.m.2024.04.003 Abstract （61）      PDF（pc） （387KB）（67）       Knowledge map    Save In this paper, we introduce and investigate certain subclass of analytic and univalent functions involving q-differintegral operator. For this function class, we give the bound estimates of the coefficients a2 and a3 and some Fekete-Szegö functional inequalities. Besides, we also estimate the corresponding symmetric Toeplitz determinants. Furthermore, we point out some consequences and connections to these results above. Related Articles | Metrics

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Normalized Ground State Solutions of Nonlinear Choquard Equations with Nonconstant Potential LI Nan, ZHAO Hui-yan, XU Li-ping Chinese Quarterly Journal of Mathematics    2024, 39 (3): 250-261.   DOI: 10.13371/j.cnki.chin.q.j.m.2024.03.003 Abstract （56）      PDF（pc） （425KB）（28）       Knowledge map    Save  In this paper, we mainly focus on the following Choquard equation...... Related Articles | Metrics

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The Gauss-Bonnet Formula of a Conical Metric on a Compact Riemann Surface FANG Han-bing, XU Bin, YANG Bai-rui Chinese Quarterly Journal of Mathematics    2024, 39 (2): 180-184.   DOI: 10.13371/j.cnki.chin.q.j.m.2024.02.006 Abstract （56）      PDF（pc） （282KB）（33）       Knowledge map    Save  We prove a generalization of the classical Gauss-Bonnet formula for a conical metric on a compact Riemann surface provided that the Gaussian curvature is Lebesgue integrable with respect to the area form of the metric. We also construct explicitly some conical metrics whose curvature is not integrable. Related Articles | Metrics

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Strong Convergence Rates of Reiterated Homogenization Problems ZHAO Jie, WU Xi-min, WANG Juan Chinese Quarterly Journal of Mathematics    2024, 39 (2): 171-179.   DOI: 10.13371/j.cnki.chin.q.j.m.2024.02.005 Abstract （54）      PDF（pc） （340KB）（24）       Knowledge map    Save  In this paper, we study the reiterated homogenization operators Lε =−div(A(x/ε,x/ε2)∇). We establish the homogenized problem and representation equation by introducing the two correctors. As a consequence, we obtain the H01 and L2 convergence estimates of solutions. Related Articles | Metrics

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The Hyers-Ulam Stability and Hyers-Ulam Instability for Some Nonhomogeneous Ordinary Differential Equations DENG Jing-tao Chinese Quarterly Journal of Mathematics    2024, 39 (4): 420-430.   DOI: 10.13371/j.cnki.chin.q.j.m.2024.04.008 Abstract （54）      PDF（pc） （341KB）（37）       Knowledge map    Save In this paper, we get a necessary and sufficient condition such that a class of differential inequalities hold. Using this necessary and sufficient condition, we prove that a class of first order nonhomogeneous ordinary differential equations have the Hyers-Ulam stability. And then, we prove that some first order nonhomogeneous ordinary differential equations and some second order nonhomogeneous ordinary differential equations do not have the Hyers-Ulam instability under some suitable conditions. Related Articles | Metrics

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The Existence of Solutions for Kirchhoff-Type Equations with General Singular Terms WANG Ji-nan, SUN Da-wei Chinese Quarterly Journal of Mathematics    2024, 39 (3): 315-323.   DOI: 10.13371/j.cnki.chin.q.j.m.2024.03.009 Abstract （53）      PDF（pc） （314KB）（24）       Knowledge map    Save We study the existence of solutions for Kirchhoff-type equations. Firstly, we use the Sobolev inequality and the weakly lower semi-continuity of the norm to prove that the corresponding function can reach the global minimum. Then, we use the variational method and some analytical techniques to obtain the existence of the positive solution of the equation when λ is small enough. Related Articles | Metrics

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On Minkowski Constants of Bouw-M¨oller Surfaces XU Yun-long, ZHONG Yu-min Chinese Quarterly Journal of Mathematics    2024, 39 (2): 185-199.   DOI: 10.13371/j.cnki.chin.q.j.m.2024.02.007 Abstract （50）      PDF（pc） （399KB）（31）       Knowledge map    Save  We consider the Bouw-M¨oller surfaces with two parameters m,n when they are not both even or m=n, n is even. We computer the e-Minkowski constant of them. Related Articles | Metrics

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A Remark on the Affine Coordinates for KdV Tau-Functions FU Zhi-peng Chinese Quarterly Journal of Mathematics    2024, 39 (3): 324-330.   DOI: 10.13371/j.cnki.chin.q.j.m.2024.03.010 Abstract （49）      PDF（pc） （259KB）（19）       Knowledge map    Save We give a proof of an explicit formula for affine coodinates of points in the Sato’s infinite Grassmannian corresponding to tau-functions for the KdV hierarchy. Related Articles | Metrics

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On the Weyl’s Lemma for Triharmonic Functions ZHENG Run-jie, ZENG Jia-min, FANG Yi Chinese Quarterly Journal of Mathematics    2024, 39 (3): 288-294.   DOI: 10.13371/j.cnki.chin.q.j.m.2024.03.006 Abstract （48）      PDF（pc） （271KB）（40）       Knowledge map    Save In this paper, by choosing some appropriate test functions, we prove the Weyl’s lemma for triharmonic functions based on the new type of mean value formulas. Related Articles | Metrics